(i) α - decay :
\(_{ Z }^{ A }{ X\rightarrow }_{ Z-2 }^{ A-4 }{ Y+ }_{ 2 }^{ 4 }{ He }\) 
(ii) β^- decay :
\(_{ Z }^{ A }{ X\rightarrow }_{ Z+1 }^{ A }{ Y+ }{ e }^{ - }+\overset { - }{ v } \)
(iii) β⁺ decay :
\({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow{ }_{\mathrm{Z}-1}^{\mathrm{A}} \mathrm{Y}+\mathrm{e}^{+}+\mathrm{v} \)
(iv) Gamma emission :
\({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X}^{*} \rightarrow{ }_{\mathrm{z}}^{\mathrm{A}} \mathrm{X}+\gamma \text { ray } \)

Binding energy per nucleon is defined as minimum energy required to take out either a proton or a neutron from nucleus.
\(\overline {BE}=\frac{BE}{A}\)

While forming a nucleus, the mass disappear is converted into energy. This energy is called binding energy of a nucleus.
\(\therefore \mathrm{BE}=\left(\mathrm{Zm}_{\mathrm{P}}+\mathrm{Nm}_{\mathrm{n}}-\mathrm{M}\right) \times \mathrm{c}^{2}\)
where, c - velocity of light
 

\(\rho=\frac{\text { mass of the nuclei }}{\text { Volume of the nuclei }}=\frac{\mathrm{Am}}{\frac{4}{3} \pi \mathrm{R}_{0}^{3} \mathrm{~A}}=\frac{\mathrm{m}}{\frac{4}{3} \pi \mathrm{R}_{0}^{3}} \)
\(\rho=\frac{1.67 \times 10^{-27}}{\frac{4}{3} \pi\left(1.2 \times 10^{-15}\right)^{3}}=2.3 \times 10^{17} \mathrm{kgm}^{-3} \)

Isobars are the atoms of different elements having the same mass number A, but different atomic number Z.
Example: \({ }_{16}^{40} \mathrm{~S},{ }_{17}^{40} \mathrm{Cl},{ }_{18}^{40} \mathrm{Ar}\)